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Multiscale Model Within-host and Between-host for Viral Infectious Diseases

Alexis Erich S. Almocera, Van Kinh Nguyen, View ORCID ProfileEsteban A. Hernandez-Vargas
doi: https://doi.org/10.1101/174961
Alexis Erich S. Almocera
Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straβe 1, 60438 Frankfurt am Main, Germany Tel.: +49-69-79847697 E-mail:
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Van Kinh Nguyen
Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straβe 1, 60438 Frankfurt am Main, Germany Tel.: +49-69-79847697 E-mail:
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Esteban A. Hernandez-Vargas
Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straβe 1, 60438 Frankfurt am Main, Germany Tel.: +49-69-79847697 E-mail:
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Abstract

Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes virus replication and the respective immune response while disease transmission is represented by a simple susceptible-infected (SI) model.

The bridge of within-to between-host is by considering transmission as a function of the viral load of the within-host level. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers Embedded Image and Embedded Imagefor the within- and the between-host subsystems, respectively. Local stability results for each subsystem, such as a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control.

Using a Lyapunov function, global stability of the between-host system was obtained. A main result was the derivation of the Embedded Image as a general increasing function of Embedded Image. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.

Footnotes

  • This work was supported by the Alfons und Gertrud Kassel-Stiftung.

  • vargas{at}fias.uni-frankfurt.de

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted August 11, 2017.
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Multiscale Model Within-host and Between-host for Viral Infectious Diseases
Alexis Erich S. Almocera, Van Kinh Nguyen, Esteban A. Hernandez-Vargas
bioRxiv 174961; doi: https://doi.org/10.1101/174961
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Multiscale Model Within-host and Between-host for Viral Infectious Diseases
Alexis Erich S. Almocera, Van Kinh Nguyen, Esteban A. Hernandez-Vargas
bioRxiv 174961; doi: https://doi.org/10.1101/174961

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